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In this talk I revisit the idea of Eilenberg (from the book Automata, Languages and machines Vol.A 1974) to use automata labelled with relations as a general computational model. The model is now called Eilenberg machines.

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Given a function as black box, where one can only query locations in the truth table of the function and each query will be charged, by querying only three locations one can tell whether the given function is linear or not with high probability.

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Motivated by the recent advent of cloud computing facilities that offer online computing power on demand, we consider a large service facility that offers simultaneous service to a large number of heterogeneous jobs, each associated with a distinc